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Two waves of different amplitudes are used in a double –slit interference experiment. In the interference pattern ratio between the intensities of bright and dark fringes is 15. Then, the ratio of amplitudes of the waves that arrive on the screen is

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$\sqrt{15} + 1$

$\sqrt{15} - 1 : 1$

$\sqrt{15}$

$\frac{\sqrt{15} + 1}{\sqrt{15} - 1}$

answer is D.

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Detailed Solution

$A = \sqrt{1}, \frac{I_{\max}}{I_{\min}} = \frac{15}{1} = {(\frac{A_{\max}}{A_{\min}})}^{2}$

$A_{1} : A_{2} = \frac{A_{\max} + A_{\min}}{A_{\max} - A_{\min}} = \frac{\sqrt{15} + 1}{\sqrt{15} - 1}$

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